hmmm.....strange.Galaxy one... but it lags on all the live wallpaper pretty much.
Yes I did a battery pull for about 10 mins.
I'm going to assume you are NOT running an anti-virus program.
I read that you were going to do a factory reset. I think at this point it certainly won't hurt since your device's performance is so degraded. I'd give it a shot (factory reset)
Let us know what you do and how it works out.